具有赫兹局域共振器的质量链中的离散呼吸子
Discrete Breathers in a Mass-in-Mass Chain with Hertzian Local Resonators
摘要：
我们报告的存在下，在一个一维的，质量中的质量链与线性intersite耦合和非线性赫兹本地谐振器，这是出于最近的研究粘附到弹性基板的微球的动力学。在理论上预测的连续和反连续极限的intersite耦合的离散呼吸子的存在下，我们使用数值延拓计算一个家庭的呼吸子插值之间的两个制度在一个有限的链，呼吸子的位移分布是本地化周围的一个或两个晶格网站。然后，我们通过对上带隙边缘附近系统的线性本征模（振幅消失）解进行数值延拓，分析呼吸子的频率-振幅依赖性。最后，我们使用直接数值积分的运动方程，以证明所确定的本地化模式的形成和演变，包括在设置，可能是相关的未来的实验研究。
英文摘要：
We report on the existence of discrete breathers in a one-dimensional, mass-in-mass chain with linear intersite coupling and nonlinear Hertzian local resonators, which is motivated by recent studies of the dynamics of microspheres adhered to elastic substrates. After predicting theoretically the existence of the discrete breathers in the continuum and anticontinuum limits of intersite coupling, we use numerical continuation to compute a family of breathers interpolating between the two regimes in a finite chain, where the displacement profiles of the breathers are localized around one or two lattice sites. We then analyze the frequency-amplitude dependence of the breathers by performing numerical continuation on a linear eigenmode (vanishing amplitude) solution of the system near the upper band gap edge. Finally, we use direct numerical integration of the equations of motion to demonstrate the formation and evolution of the identified localized modes, including within settings that may be relevant to future experimental studies.
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